Mathematically, different models are available to model two phase flows, each with its own benefits and difficulties.
In diffuse interface models such as the Navier-Stokes-Korteweg model, the phase interface is smeared over a certain distance and the interface width is incorporated in the underlying energy potential,
see, e.g., Refs. [1]}, [2]} and the references therein.
So called phase field models have an individual evolution equation for the phase field coupled to the equations governing the flow dynamics, see, e.g., Refs.  [3]}, [4]}.
A widely used class models the flow as a diffuse mixture, see Refs. [5]}, [6]}, [7]}, [8]}. For further reading and a comparative study we also refer to Zein et al.[9]}.
